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Optics and Lasers in Engineering 40 (2003) 263–288 An experimental study of impact-induced failure events in homogeneous layered materials using dynamic photoelasticity and high-speed photography L. Roy Xu a, *, Ares J. Rosakis b a Department of Civil and Environmental Engineering, Station B351831, Vanderbilt University, Nashville, TN 37235, USA b Graduate Institute of Technology, California Aeronautical Laboratories, Pasadena, CA 91125, USA Abstract The generation and the subsequent evolution of dynamic failure events in homogeneous layered materials that occur within microseconds after impact were investigated experimen- tally. Tested configurations include three-layer and two-layer, bonded Homalite specimens featuring different bonding strengths. High-speed photography and dynamic photoelasticity were utilized to study the nature, sequence and interaction of failure modes. A series of complex failure modes was observed. In most cases, and at the early stages of the impact event, intra-layer failure (or bulk matrix failure) appeared in the form of cracks radiating from the impact point. These cracks were opening-dominated and their speeds were less than the crack branching speed of the Homalite. Subsequent crack branching in several forms was also observed. Mixed-mode inter-layer cracking (or interfacial debonding) was initiated when the intra-layer cracks approached the interface with a large incident angle. The dynamic interaction between inter-layer crack formation and intra-layer crack growth (or the so-called ‘‘Cook–Gordon Mechanism’’) was visualized for the first time. Interfacial bonding played a significant role in impact damage spreading. Cracks arrested at weak bonds and the stress wave intensity was reduced dramatically by the use of a thin but ductile adhesive layer. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Impact failure; Layered materials; Interfacial bonding; Dynamic photoelasticity; High-speed photography *Corresponding author. Fax: +1-615-322-3365. E-mail address: [email protected] (L.R. Xu). 0143-8166/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII:S0143-8166(02)00093-3

An experimental study of impact-induced failure events in homogeneous layered materials using dynamic photoelasticity and high-speed photography

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Optics and Lasers in Engineering 40 (2003) 263–288

An experimental study of impact-inducedfailure events in homogeneous layered

materials using dynamic photoelasticity andhigh-speed photography

L. Roy Xua,*, Ares J. Rosakisb

aDepartment of Civil and Environmental Engineering, Station B351831, Vanderbilt University, Nashville,

TN 37235, USAb Graduate Institute of Technology, California Aeronautical Laboratories, Pasadena, CA 91125, USA

Abstract

The generation and the subsequent evolution of dynamic failure events in homogeneous

layered materials that occur within microseconds after impact were investigated experimen-

tally. Tested configurations include three-layer and two-layer, bonded Homalite specimens

featuring different bonding strengths. High-speed photography and dynamic photoelasticity

were utilized to study the nature, sequence and interaction of failure modes. A series of

complex failure modes was observed. In most cases, and at the early stages of the impact event,

intra-layer failure (or bulk matrix failure) appeared in the form of cracks radiating from the

impact point. These cracks were opening-dominated and their speeds were less than the crack

branching speed of the Homalite. Subsequent crack branching in several forms was also

observed. Mixed-mode inter-layer cracking (or interfacial debonding) was initiated when the

intra-layer cracks approached the interface with a large incident angle. The dynamic

interaction between inter-layer crack formation and intra-layer crack growth (or the so-called

‘‘Cook–Gordon Mechanism’’) was visualized for the first time. Interfacial bonding played a

significant role in impact damage spreading. Cracks arrested at weak bonds and the stress

wave intensity was reduced dramatically by the use of a thin but ductile adhesive layer.

r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Impact failure; Layered materials; Interfacial bonding; Dynamic photoelasticity; High-speed

photography

*Corresponding author. Fax: +1-615-322-3365.

E-mail address: [email protected] (L.R. Xu).

0143-8166/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 4 3 - 8 1 6 6 ( 0 2 ) 0 0 0 9 3 - 3

1. Introduction

Layered materials and structures have promising applications in many importantfields of engineering. These include, among others, the use of advanced compositelaminates in aerospace engineering; sandwich structures in naval engineering; andmulti-layered thin film structures in micro-electronic-mechanical systems. In anentirely different length scale such materials are also found in the complex layeredrock structures of earth’s crust. While failure characteristics of layered materialssubjected to static loading have been investigated extensively in past years [1], theirdynamic counterparts have remained elusive. Our current research interest focuseson studies of such dynamic failure events in layered materials and, in particular, onthe identification of the chronology and sequence of these events. For most layeredmaterials, the presence of highly complicated dynamic failure modes and theinaccessibility of internal damage to real-time scrutiny has resulted in experimentalstudies of only the final impact damage characteristics and to the measurement ofpost-mortem residual strengths [2–4]. Hence, the sequence and nature of failureprocess have never been properly clarified.

For many simple engineering structures subjected to static or dynamic loading,computational and analytical models can be employed to provide realisticapproximations of the physical failure processes under investigation. However, thismay not be possible when more complex geometries, involving layered materials orconfigurations, need to be investigated. For such more complex cases, modelexperiments may prove extremely useful as intermediate steps, which reveal the basicphysics of the problem and provide relatively straightforward validation ofcomputational models before such models are applied to predictions of the fullycomplex failure situations. A striking example of the role of model experiments wasprovided by Riley and Dally [5], who designed a model metal/polymer layeredspecimen subjected to dynamic loading. Their model configuration was designed tosimulate dynamic loading and stress wave evolution in complex layered structures.

In our experiments, we adopt and extend the same concept and to that effect weintroduce an appropriate intermediate model configuration, which allows us, inaddition to stress wave loading, to study the basic dynamic failure mechanismsinvolved in a layered structure. Indeed, in order to simulate the difficult 3-D problemof the out-of-plane impact of real layered structures and at the same time preservethe essence of the failure phenomena involved, we propose a two-dimensional, planestress specimen, which represents a cross-sectional cut from a layered structure asillustrated in Fig. 1. For this type of model specimens, failure processes are easy torecord, visualize and analyze. It is noted that although the exact impact mechanicsinvolved in these two configurations are not identical (mainly because ofdimenionality constraints), the general mechanisms of stress wave propagationand failure progress of the real and model layered materials are quite similar.

As discussed by Xu and Rosakis [6], in designing these model two-dimensionalspecimens, it is important to select model materials whose elastic mismatch is similarto that of materials used in real engineering applications. Selecting similar Dundurs’parameters [1] may ensure similarity of the elasto-static response. Meanwhile,

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288264

selecting model material combinations with similar ratios of wave speeds as the realstructure is important in considering similarity of their elasto-dynamic behaviors.These two issues form similarity rules to connect real structures and experimentalmodels. In the present investigation, we only study layered materials composed ofone kind of homogeneous material. For this zero stiffness-mismatch case, bothDundurs’ parameters vanish and the ratio of wave speeds is unity. The resultinglayered structure is constitutively homogeneous and it only features planes ofstrength and fracture toughness inhomogeneity (bonds lines) between layers. In theabsence of constitutive material property mismatch, our major purpose is only toexplore the effect of interfacial bonding on the development of dynamic failuremechanism in layered materials.

The objectives of the current work are to conduct systematic experimental studiesof the time evolution and the nature of different failure events and to investigate theinteraction of these dynamic failure modes in real-time. Through these modelexperiments, we try to provide guidance for the construction of theoretical modelsand validation of numerical codes.

2. Experimental program

2.1. Materials and specimens

Homalite-100 was selected as our model photoelasticity material. Some of itsphysical properties are listed in Table 1. The quasi-static values are obtained fromthe literature while the dynamic values are measured by the procedure outlined inSection 3. The dynamic fracture characteristics of bulk Homalite-100 have been wellinvestigated in the past decades [7–10]. Here, we mainly pay attention to the dynamicfailure modes of Homalite in layered form. To provide different interfacial strengthsand fracture toughnesses, four kinds of adhesives, Weldon-10 and Loctite 330, 384and 5083, were used to bond the interfaces [11]. The interfacial bond strengths andthe fracture toughness for those adhesives are listed in Table 2. The Weldon-10 andLoctite 330 are considered to be ‘‘strong’’ adhesives. The Loctite 384 can form an

Fig. 1. 3-D problem and plane stress idealization.

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‘‘intermediate strength’’ bond while the Loctite 5083 gives a ‘‘weak bond’’. Thethickness of the final adhesive layer is o20 mm. Loctite 5083 adhesive is alsoconsidered to be a ductile adhesive since its elongation at failure (as measured by themanufacturer) in cured bulk form is 170% or two orders of magnitude higher thanthe rest of the adhesives.

Three different types of specimens were designed and tested. As shown in Fig. 2,type-A specimens have two layers with equal layer widths, and type-B specimensinvolve two layers with one layer twice as thick as the other. Type-C specimens weredesigned to have two bonding interfaces and three equal-width layers. All three typesof specimens have the same out-of-plane thickness of 6.35 mm (0.25 inch) and thesame length of 254 mm (10 inches). In general, each layer width is 33 mm except for afew specimens in which w1 ¼ 38:1mm.

2.2. Experimental setup

A schematic of the dynamic photoelasticity setup used in this study is given inFig. 3. Two sheets of circular polarizer were placed on either side of the specimen.An Innova Sabre argon-ion pulsed laser was used as the light source. The laser wasset to operate on a single wavelength—514.5 nm (blue–green light). At thiswavelength, the continuous power output of the laser is 8W. The laser emits an

Table 1

Material properties of Homalite–100

Homalite 100

Property Static (strain rate B10�3/s) Dynamic (strain rate B103/s)

Density r (kg/m3) 1230 1230

Young’s modulus (GPa) 3.45

Dilatational wave speed cl (m/s)

(plane stress)

1890 2119

Shear wave speed cs (m/s) 1080 1208

Rayleigh wave speed cR (m/s) 1010 1110

Poisson’s ratio n 0.35 0.35

Material fringe constant fs (kN/m) 23.7

Table 2

Interfacial strengths and model I fracture toughness of different bonds

Interface Tensile

strength sc (MPa)

Shear strength

tc (Mpa)

Fracture toughness

(MPam1/2 ) GIC (J/m2)

Homalite//Weldon-10//Homalite 7.74 >21.65 0.83 199.7

Homalite//330//Homalite 6.99 12.58 0.93 250.7

Homalite//384//Homalite 6.75 7.47 0.38 41.9

Homalite//5083//Homalite 1.53 0.81 0.19 10.5

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intense beam of 2mm diameter, which is 100:1 vertically polarized. An acousto-opticmodulator (Bragg cell) is placed in front of the laser to produce a pulsed output. Theduration of each laser pulse can be varied between 8 and 20 ns. During the impactexperiment, the acousto-optic modulator is driven by the high-speed camera tocontrol the timing of each laser pulse, so that it coincides with the times the cameraoptics are aligned to expose a particular frame on the film track. An electro-mechanical shutter is placed in front of the laser to prevent the light ‘‘leaking’’through the Bragg cell from exposing the film before or after the experiment. A widegap sensor mounted on the gas gun barrel about 1 in from the end is used totrigger the shutter opening for a short duration (around 10 ms). A strain gagebonded to the specimen at the impact side was used to trigger recording by thehigh-speed camera. The coherent, monochromatic, plane polarized light outputis collimated to a beam of 100 mm diameter. The laser beam is transmittedthrough the specimen. The resulting fringe pattern is recorded by the high-speedcamera.

Fig. 2. Model specimen geometries: (a) two-layer specimens with equal widths (type-A), (b) two-layer

specimens with W2 ¼ 2W1 (type-B), and (c) three-layer specimens with equal widths (type-C).

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A Cordin model 330A rotating mirror type high-speed film camera was used torecord the images. The high-speed camera contains a rotating mirror that directs theimage on to the film mounted on a film track surrounding it. The rotating mirror isdriven by a gas turbine running on compressed helium. Individual frames areexposed sequentially by inducing the laser to produce a high-powered pulse of shortduration and when the rotating mirror is aligned to a particular frame. The camerarecords 80 distinct images at frame rates of up to 2 million per second. A feedbacksignal from the turbine is fed to a 10 KHz frequency counter, which allows a precisemonitoring of the turbine speed. Also, the synchronizing signal sent by the camera tothe acousto-optic modulator is simultaneously routed to a HP digital oscilloscope toobtain a record of the timings of each individual laser pulse. Kodak TMAX 400black and white film was used to record the fringe patterns. The optical system in thehigh-speed camera introduces an elliptical distortion to the recorded films. For acircular original image, the recorded image is an ellipse with its major axis about15% larger in comparison with the minor axis. The developed negatives werescanned using a negative scanner and the elliptical distortion was removed digitally.

During the impact test, a projectile was fired by the gas gun and hit the specimenor a steel buffer to trigger the recording system. Under the dynamic deformation, thegeneration of isochromatic fringe patterns is governed by the stress optic law. Forthe case of monochromatic light, the condition for the formation of isochromatic

Fig. 3. Schematic of the dynamic photoelasticity setup.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288268

interference fringes can be expressed as [7]

#s1 � #s2 ¼Nfs

h;

where #s1 � #s2 is the principal stress difference of the thickness averaged stress tensor,fs is the material fringe value which is listed in Table 1, N is the isochromatic fringeorder and h is the half specimen thickness. The isochromatic fringe patterns observedare proportional to contours of constant maximum shear stress, #tmax ¼ ð #s1 � #s2Þ=2:

2.3. The three-lens system

In order to observe remote failure event interactions, a large field of view isnecessary. However, our Cordin 330A camera has a long front optical tube and itsmaximum view angle 2b is 41 as shown in Fig. 4. If a single lens is used, themaximum size of the field of view is 2f tan ðbÞ; were f is the focal length of the lens.In order to minimize shadow spot formation, f should be chosen to be a small valuebased on our practical experience. As a result, the resulting field of view will be toosmall for full specimen visualization. To overcome this problem, a three-lens systemis employed as shown in Fig. 4. In this system, the first lens facing the 100 mm laserbeam is a plano-convex lens whose focal length is 380 mm. The second lens is aplano-concave lens whose focal length is 100 mm. Lenses 1 and 2 share the samefocal point at one side and, as a result, a parallel beam of reduced diameter isformed. This beam passes through a bi-convex lens (lens 3) of focal length 500 mm.The resulting converging beam incident angle is o21 and satisfies our statedrequirement. Hence, the full 100 mm beam can enter the long camera tube.

Another restriction governing the choice of lens types and focal lengths comesfrom aberration balancing. Here, the convex side of lens 1 and the planar side of lens2 must face the laser beam to cancel part of the aberration. The most significantshortcoming for this three-lens system is its alignment sensitivity. In addition, lightintensity is somewhat reduced after the beam passes from this multiple lensesarrangement. So, this system was used only for those experiments, which required alarge field of view.

Fig. 4. The three-lens system used in large field of view experiments. (1) plano-convex lens, (2) plano-

concave lens, and (3) bi-convex lens.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288 269

3. Results and discussion

Homalite-100 is a rate sensitive viscoelastic solid and its wave speeds depend onstrain rate as indicated in Table 1. Wave speed differences of approximately 17% areexpected over six orders of magnitude differences in equivalent strain rate. In orderto obtain a more accurate measure of the wave speed levels relevant to our impactexperiments, a calibration test was undertaken. A Homalite plate was impacted at aprojectile speed of 24 m/s and the impact area was imaged by the high-speed camera.The photoelastic fringe pattern corresponding to this dilatational front spreadthrough the material and the location of its front was traced and plotted as afunction of time (see Fig. 5). The resulting linear variation reveals a constantdilatational wave speed of approximately 2119 m/s which, for a Poisson’s ratio of0.35, corresponds to a shear wave speed of 1208 m/s and a Rayleigh speed of 1110 m/s. Fringe patterns of the type shown in Fig. 5 have also allowed us to estimate thelocal strain rate at the impact point. For the impact speeds used in this paper, thestrain rate was found to be of the order of 103/s. As expected these values are higherthan the ones corresponding to a quasi-static loading (strain rate B10�3/s) and arelisted in a separate column of Table 1. From now on indicated wave speeds willcorrespond to the above measured dynamic values.

3.1. The two-layer specimen with equal layer widths subjected to mitigated projectile

impact

Fig. 6 shows a series of photoelasticity snap shots following impact of a type-Aspecimen. In all experiments reported in this section, the projectile impacted thecenter of the bottom layer on a steel buffer as shown in Fig. 6(a). The horizontal linein the field of view reveals the position of the interface in which the dark circularspot, at the lower left-hand side just below the interface, is a scaling mark of 6.35 mm

Fig. 5. Measured stress wave front location versus time used to estimate the longitudinal wave speed of

the Homalite-100 subjected to the current impact strain rate regime.

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in diameter. Fig. 6(b) shows a fan of mode I cracks (symmetric fringe patterns)appearing from the upper free edge at approximately 93.8 ms after impact. Generally,the whole recording system has a delay and its timing error is within 10 ms. Afterimpact, the longitudinal compressive stress wave traveled from the lower impact sidetowards the upper free edge. This compressive stress wave reflected from this edge asa tensile wave and its intensity was sufficient to nucleate a fan of branched cracksfrom the free edge. As time goes on (Fig. 6(c)–(f)), the nucleated fan of cracks widenssignificantly by producing a multiplicity of both successful and unsuccessfulbranches (for a discussion of crack branching phenomenon in bulk Homalite, see

Fig. 6. Dynamic failure process in a two-layer specimen showing the interaction of a fan of mode I

incident cracks and the resulting interfacial crack. The thin horizontal line is the weak interface. The

circular dot at the left low position in every photo is the scaling mark bonded on the specimen.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288 271

Ravi-Chandar and Knauss [10]), some of which move towards the still coherentinterface. The average speed of these locally mode I, branched cracks is 0.41 CS;which is the branching speed in bulk Homalite.

Well before the branched cracks reached the interface, a central inter-layer crackwas nucleated at the intersection of the specimen centerline and the bond line as seenin Fig. 6(c). This interfacial crack propagated in both directions off the center asshown in Fig. 6(d). At the specimen centerline, the shear stresses vanish because ofsymmetry. As a result, the nucleated inter-layer crack is initially and, for a very shorttime, mode I dominated. Its nucleation is induced by the stress field produced by thefan of branched cracks approaching the interface. As this crack spreadssymmetrically, opening up the interface (see distinct evidence of decohesion inFig. 6(f)), the fan of branched cracks discelerates and arrests just before these cracksreach the decohered interface. The above described scenario is perhaps the first real-time visualization of the dynamic equivalent of the ‘‘Cook–Gordon Mechanism’’ [12]describing the remote decohesion of an interface due to the approach of a matrix(intra-layer) crack.

As the interfacial crack spreads away from the specimen centerline, it almostimmediately encounters increasing amount of interfacial shear stress, which quicklyconverts it to a mixed-mode and eventually to a mode II dominated crack. Unlikepropagating cracks in bulk Homalite, interfacial cracks are constrained to propagatealong the weak interface and, as a result, they can do so under mixed-mode orprimarily mode II conditions. They can also propagate at very high (even inter-sonic)speeds compared to their bulk (intra-layer) counterparts. This phenomenon hasrecently been investigated experimentally by Rosakis et al. [13] and numerically byNeedleman [14] and by Geubelle and Kubair [15]. To illustrate this point, thevariation of the left interfacial crack tip position versus time and the correspondingcrack tip speed are plotted in Fig. 7(a) and (b), respectively. Indeed this figure showsvery high interfacial crack tip speeds initially well within the intersonic regime (crackspeed is greater than the shear wave speed but less than the longitudinal wave speedof the bulk material), later decelerating to a large fraction of the Rayleigh wavespeed. This observation is consistent with the surmised shear-dominated nature ofthis crack (see Geubelle and Kubair [15]). If this inter-layer crack is, at least for shorttimes, intersonic, the photoelastic images obtained here should reveal the existence ofshear shock wave discontinuities emitted from the propagating crack tips andinclined at an angle b ¼ sin�1ðCs=V Þ to the interface (Rosakis et al. [13]). Indeed, aclose look at Fig. 6(d) and (e) reveal the existence of such shear shock waves, whichare shown in detail in Figs. 8(a) and (b). The angle b can now be used to provide anindependent measure of the ratio, V=Cs of the instantaneous crack tip speed to theshear wave speed. This ratio is plotted in Fig. 8(c) as a function of time (blacktriangles). For comparison purposes, the same ratio, obtained from the independentmeasurement of the crack length record is also shown. The two sets of points areobtained by using crack speeds from Fig. 7 and the quasi-static and the dynamicvalues of Cs; from Table 1, respectively. As evident from this composite plot, thetrends are very consistent. Differences are due to experimental errors introducedthrough differentiating the crack length record, and uncertainties in shear wave

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288272

speed choice. Indeed very near the crack tip where the strain rates are very high,the dynamic values of shear wave speed should be used; while further away thestatic values may be more appropriate for shock angle estimation (Abraham andGao [16]).

Additional evidence of the shear-dominated nature of the interfacial cracks isprovided by the nucleation and growth of a periodic array of secondary microcracksobserved to occur along the bond at a certain distance from the centerline of thespecimen (see Fig. 6(f)). These microcracks are generated just behind thepropagating shear crack tip (see Fig. 9) and spread at a steep angle of approximately111 to the normal of the bonded interface. They are locally mode I cracks and theygrow only at the bottom layer side of the interface indicating that this layer isprimarily in tension along the horizontal direction. Their opening nature is evident

Fig. 7. History of inter-layer crack length (a) and speed (b) of the two-layer specimen (2lhhwswd-b1). The

two horizontal lines correspond to the dynamic values of the shear and Rayleigh wave speeds of Homaite-

100 shown in Table 1.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288 273

from the existence of symmetric and almost circular caustics surrounding their tips(see Fig. 9). The generation of such secondary cracks following shear interfacialcrack growth was first discussed by Rosakis et al. [17] and Samudrala et al. [18] inconnection to intersonic shear rupture of Homalite/Homalite interfaces. Asdiscussed in these references, their 111 inclination indicates the existence of frictionalcontact and sliding behind the growing shear crack faces, which slightly change theprincipal stress directions responsible for path selection for the microcracks.

For the present discussion, the existence of such secondary cracks in impactedlayered specimens is also very important. It shows how different failure modes (somesymmetric and others shear-dominated) may interact and trigger each other in a non-straightforward way to result in the final brittle failure of a layered structure. Indeedin the processes discussed above, damage was first initiated by the mode I dominatedfan of branched cracks moving towards the interface. Without penetrating the

Fig. 8. Early stages of intersonic, interfacial crack growth revealing the existence of shear shock waves

(a, b) and the estimated interfacial crack speeds using different methods (c).

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288274

interface, this fan of opening crack induced inter-layer failure which in turntransitioned from an opening mode to a shear mode as it moved away from thecenterline and as it delaminated the interface. Finally, it was this shear-dominateddelamination stage which made it possible for the periodic sequence of openingmicrocracks to penetrate the bottom layer and cause its final fragmentations.

3.2. The two-layer specimen with equal layer widths subjected to direct projectile

impact

Fig. 10 shows a series of images for a two-layer specimen subjected to directprojectile impact. Stress wave propagation and reflection from the top free edge isshown in Fig. 10(b). The fringe pattern at the bonded interface is continuous anddoes not even exhibit any discontinuities in slope. This implies a good bonding andmatched material properties of the Homalite and the bonding adhesive. Unlike theprevious specimen with a mitigating steel buffer at the impact point, a dark zone ofdiffuse damage was observed at the impacted side. This dark zone is a highlycompressed zone of comminuted material created by the direct projectile impact.Due to the large out-of-plane deformation, the light rays transmitted through thisarea cannot be collected by the high-speed camera, thus producing a massive shadowspot. It is also noticed that a ‘‘plastic deformation ring,’’ initially propagating atapproximately 118 m/s, appeared at approximately 76 ms (Fig. 10(c)). Across thisring, permanent discontinuities of the fringe pattern were observed, indicating theirreversible damage nature within this semi-circular region. At the first stages of itsevolution, the plastic semi-circle was smooth and transparent. As time evolvedseveral radial mode I cracks radiating from the impact point crossed the ringboundary moving towards the upper free edge of the specimen. With increasing time,the initial transparency of the plastically deformed area surrounded by the ring was

Fig. 9. A detailed view of the formation of secondary opening microcracks following shear dominated

interfacial delamination.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288 275

compromised by the spreading of more complex 3-D damage modes. This becameobvious through post-mortem inspection of the impacted plates where large 3-Dsurface cracks propagating in the specimen thickness (parallel to the plate freesurface) were identified. It is the evolution of such cracks and their slightly wavynature that produce the ‘‘shell’’ like structure of the further damaged plastic semi-circle in Fig. 10(e) and (f).

3.3. Failure process in a two-layer specimen with unequal layer widths

Post-mortem pictures of damage resulting from impact of two, type-B, specimensare shown in Figs. 11(a) and (b). The only difference between these two specimens,

Fig. 10. Failure process of a two-layer specimen (2lhhsp384-1) subjected to direct projectile impact.

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288276

subjected to identical impact histories, is the strength of interfacial bonding. It isobvious from this figure that the interfacial bonding plays a significant role in theoverall dynamic failure process. For the specimen with the intermediate strengthinterface as shown in Fig. 11(a), there are many branched, locally mode I, cracksradiating from the site of impact. Some of these I cracks only passed through theinterface and did not cause any debonding. In contrast, the specimen with the weakinterface, shown in Fig. 11(b), features fewer cracks radiating from the site ofimpact. Two of these cracks arrested at the weak interface, while the third producedonly partial interfacial debonding.

Fig. 12 shows a sequence of real-time images of the dynamic failure progress of thelayered Homalite structure (type-B) featuring only one weak interface bond. Thiscase corresponds to the post-mortem pattern of Fig. 11(b). In this sequence, the tophorizontal line is the interface while the bottom line is a camera streak line of no

Fig. 11. Post-mortem failure patterns of two identical specimens with different interfacial bond strengths

subjected to the same impact speed of V ¼ 20m/s. (a) 2LHHSP384-LT1 (two-layer system with 384

intermediate strength bonding and impact at the large width layer), (b) 2LHHSP5083-LT1 (with 5083

weak bonding).

L.R. Xu, A.J. Rosakis / Optics and Lasers in Engineering 40 (2003) 263–288 277

significance to the physical process. Fig. 12(b) reveals that the number of fringes orthe stress wave gradient across the interface was dramatically reduced by the thin butsoft adhesive film of 20 mm in thickness. After a long time period (380 ms) of wavemotion within these two layers, a crack initiated from the dark impact zone wasobserved near the site of impact. This crack accelerated and eventually branched asshown in Fig. 12(d). As soon as the resulting branches approached the interface, theyeither arrested or turned into it producing partially interfacial debonding as shown inFigs. 12(e) and (f). The exact reasons of the inability of these cracks to penetrate the

Fig. 12. Crack propagation and arrest at a two-layer specimen with 5083 weak bonding. The central black

line is the camera streak reference line. The upper horizontal line is the only interface.

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upper layer are complex and are currently under investigation. However, the pivotalrole of the weak interface in triggering this behavior is clearly evident. This mayprovide a useful design methodology to prevent the spread of impact damageresulting from low-speed projectiles. In an early study of impact mechanisms ofcomposite laminates, Sun and Rechak [19] investigated a similar phenomenon byplacing adhesive layers between plies, and thus delaying or even suppressing dynamicdelamination.

In the case discussed above, the impact side was far away from the interface. If wenow use the same specimen geometry and projectile loading history but insteadimpact the side close to the bonded interface, the resulting failure patterns are verydifferent. This is evident from the post-mortem reconstructions of three bi-layerspecimens (impacted close to the interface) with the same geometrical dimensions butdifferent interfacial bonding strengths, which are presented in Fig. 13. It should firstbe emphasized that two identical specimens with the same interfacial bonding havequite different failure patterns if the impact location is reversed. This is evident bycomparing Fig. 11(a) with Fig. 13(b) as well as Fig. 11(b) with Fig. 13(c). Differencesare most pronounced for specimens with intermediate strength bonding shown inFigs. 11(a) and 13(b). Indeed more radial cracks were found and more extensiveinterfacial debonding occurred when the specimen was impacted closer to the bond.In the case shown in Fig. 13(b), it is also observed that cracks radiating from theimpact point approached the bond with different incident angles (the angles betweenthe crack path and the interface) and triggered a variety of subsequent failurebehaviors. Those cracks with large incident angles penetrated the interface, but thosecracks with small incident angles deflected into the interface and led to shear-dominated debonding, similar to the shear decohesion phenomenon discussed inSection 3.1. Here again, a close look at the upper side of the decohered interfacereveals a periodic sequence of tensile microcracks inclined at small angles to theinterface normal. These tensile microcracks are again generated as some of the radialcracks deflect into the interface, becoming shear-dominated and decohering itthrough a process of dynamic shear failure. The microcracks are generated justbehind the growing shear interfacial cracks at the tension side of the interface. Areal-time view of the failure process corresponding to an intermediate strength bondis provided in Fig. 14. The first failure event visualized in this sequence is the zone ofcomminuted and plastically deformed materials (dark area) as evident fromFig. 14(b). As time progresses, more than ten intra-layer radiating cracks appearand most of them pass through the interfacial bonding. The radial cracks thatapproached with a smaller incident angle, and were deflected into the interface,moved along it with higher speeds as evident by the elongated shape of the failurefront arc shown in Fig. 14(c).

3.4. Failure process in a three-layer specimen with equal layer widths

Failure patterns became more complicated as a second interface was introduced toconstruct the three-layer specimens (type-C), shown in Fig. 15. Figs. 15(a) and (b)display post-mortem images of damage of two identical specimens featuring a strong

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bottom interface and a top interface of two different (intermediate and weak)strengths, respectively. For the specimen with intermediate top interface (Fig. 15(a)),radial cracks initiated at the impacted layer and passed through the lower (strong)and the upper (intermediate) interfaces. Also, several cracks were able to cross all theway to the layer farthest from the impact side. In contrast, the specimen with theweak top interface, shown in Fig. 15(b), featured fewer radial cracks on the impactedside. Also, those cracks were arrested at the upper weak interface and did notpenetrate into the upper layer. Extensive interfacial debonding at the upper interfacewas observed. The two specimens in Fig. 15(a) and (c) are identical except for thechoice of impact side. In Fig. 15(a), the impact side is closer to the strong interface.

Fig. 13. Post-mortem failure patterns of three bi-layer specimens with different interfacial bonding

strengths subjected to the same impact speed of V ¼ 21m/s. (a) 2LHHSP330ST1, (b) 2LHHSP384ST1,

and (c) 2LHHSP5083ST2.

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So the radiating cracks mainly passed through this strong interface, causingdebonding, only in the central portion of the specimen. Again debonding is shear-dominated because microcracks are visible along this decohered part of the strongbond.

A real-time view of the failure process of the specimen in Fig. 15(a) was presentedin Fig. 16. In Fig. 16(b) the stress wave propagates through both upper and lowerinterfaces without experiencing any strong fringe or weak fringe slope disconti-nuities. In these photographs, the central thin line adjacent to the small circular markis the camera streak line and is an artifact of the optical setup. The other two thinlines represent strong and intermediate strength interfaces. A group of radial crackssoon propagate through the lower, strong, interface as shown in Fig. 16(d) and (e).Those radiating cracks with large incident angles passed through the lower, stronginterface and subsequently penetrated the upper, intermediate strength interface.Those few cracks that approached with smaller incident angles were deflected intothe interface and one of them (moving to the right) is clearly shown in Fig. 16(d). Toillustrate this phenomenon, an enlarged part of the specimen shown in Fig. 15(c) is

Fig. 14. A group of cracks initiated and propagated in a bi-layer Homalite specimen (2lhhsp384st1) with

intermediate strength bonding. The lower thin line is the bonded interface. The upper horizontal line is a

camera streak line.

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presented in Fig. 17. For two cracks with different incident angles, different failureevents were observed. The crack with the large incident angle of 781 passed throughthe interface. However, the crack with the small incident angle of 501 could notpenetrate the interface and created interfacial debonding. A systematic study of thisproblem is presently underway by the authors [20].

We now turn attention to tri-layer specimens involving at least one weak bond (the5083 adhesive in Table 2). As clearly shown in Fig. 18, this adhesive is weak andductile enough (see Section 2.1) never to allow crack penetration into the next layerunder low-speed impact. In Fig. 18(a) some radial cracks from the impact region

Fig. 15. Failure patterns of the three-layer specimens with different bonding and impact sides. (a)

3LHHSP330384-3302, (b) 3LHHSP330583-3301, and (c) 3LHHSP330384-3841. Notice specimens (a) and

(c) are identical cases except for the different impact sides.

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penetrate the intermediate strength bond of the lower interface (primarily near thecenter where the incident angle is large). Some interfacial debonding also occurs andis triggered by the radial cracks that approach the interface with more shallowangles. However, the situation at the upper, weak interface is very different. Asradial cracks approach the weak bond, they are completely arrested neitherpenetrating nor causing debonding of this second interface. This is also found to be

Fig. 16. Failure process of specimen 3LHHSP450384-3302. (The lower and upper thin lines are

intermediate and strong interfaces.)

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true in all other cases (such as Fig. 18(b) and (c)) where such a weak and ductile bondis involved. In all of these cases, the bond was never penetrated nor was there anyvisible decohesion, at least at an impact speed of 21 m/s. This speaks of an apparentductility of this bond whose extend will be investigated next.

In order to further test the impact resistance of specimens with 5083 weak butductile adhesive bonds, a three-layer specimen containing two identical 5083interfaces was designed and subjected to different impact speeds. The post-mortempictures are shown in Fig. 19. The impact speeds were 20 and 46 m/s, respectively.Although the size of the local impact damage zone is quite different, in both cases thebond was again neither penetrated nor compromised. The impact damage is stilllimited inside the layer impacted directly by the projectile. The other two layers arestill perfectly bonded.

To understand the effect of the introduction of a ductile adhesive bond as amechanism for failure prevention, real-time visualization was undertaken in Fig. 20.As shown in Fig. 20(b), the stress wave intensity across the interface was reduceddramatically after the first interfacial 5083 bonding was encountered. In Fig. 20(c),the stress wave intensity was further reduced after the second 5083 interfacewas crossed. Meanwhile, complicated stress wave movement is seen in Fig. 20(d)and the dark contact zone is continuously growing. Radial cracks are initiatedfrom the impact point very early (around 70 ms) compared to the other three-layer specimens shown in Fig. 16. However, those cracks soon arrested at theinterface as seen in Fig. 20(e) and (f). No interfacial debonding was found inthis type of specimens. In our investigation, only low-impact speed tests wereconducted.

Fig. 17. Intra-layer cracks hit the interface with different angles (specimen 3LHHSP330384-3841). The

crack with a large incident angle penetrated the interface while the crack with a small incident angle

deflected at the interface.

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4. Summary and conclusions

We investigate the generation and time evolution of dynamic failure modes inlayered materials composed of bonded layers of Homalite-100. We observe a varietyof dynamic failure mechanisms in the form of either intra-layer (matrix) cracks orinter-layer (interfacial) cracks or debonding. Dynamic intra-layer failure is always ofthe symmetric (mode I) type and it often involves multiple branching events.Dynamic inter-layer fracturing or debonding is almost always shear-dominated and

Fig. 18. Comparison of final pattern of the three-layer specimens with 5083 bonding with the same impact

speed of 21m/s. (a) 3LHHSP384583-3841, (b) 3LHHSP330583-5831, and (c) 3LHHSP384583-5831.

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spreads at much faster speeds than intra-layer failure. One of the themes common toall cases studied here is the interrelation and interaction between these differentsymmetric and asymmetric failure modes. Indeed it is often the case that symmetric(mode I) intra-layer cracks approaching an interface (even if they never penetrate it)trigger mixed-mode or mode II interfacial delaminations, which in turn laterallyspread mode I damage by an interesting mechanism of microcrack formation. Inother cases, and depending on relative bond strengths and angles of incidence, intra-layer (matrix) cracks may clearly penetrate an interface without delaminating it.

In this paper, we explore some of these phenomena, and their interrelation, inperhaps the simplest, non-trivial, setting possible. We intentionally choose layers ofidentical material constitution in order to eliminate wave speed and other propertymismatches across interfaces. We instead concentrate in varying bond strengths,layer geometry and to some extend impact speed. The above described, real-time

Fig. 19. Effect of the impact speed to failure patterns of the three-layer specimens featuring two weak but

ductile adhesive bonds.

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observations of failure modes in layered solids, in addition to identifying some newbasic failure phenomena, can perhaps serve as benchmark experiments for thevalidation of complex numerical codes designed to model dynamic failure of layeredstructures.

Fig. 20. Impact damage progress and wave propagation in a three-layer specimen featuring two 5083

weakly bonded interfaces (3LHHSP583-2).

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Acknowledgements

The authors gratefully acknowledge the support of the Office of Naval Research(Dr. Y.D.S. Rajapakse, Project Monitor) through a grant (#N00014-95-1-0453) toCaltech.

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